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Abstract One of the key problems in multi-scale homogenization modeling based on the average-field theory is the proper prescription of boundary conditions on the representative volume element (RVE), with which the Hill-Mandel condition, i.e. the Hill’s macro-homogeneity condition, can be satisfied. From the existing contribution to the heterogeneous Cosserat continuum, only mixed translational displacement-surface couple boundary condition can be prescribed. While other commonly used RVE boundary conditions, such as uniform translational and rotational displacement boundary conditions and periodic RVE boundary conditions, can not be used. That holds back the development and application of the corresponding homogenization method. On the basis of derivation of a new version of Hill’s lemma, this paper gives more versatile RVE boundary conditions in the strong form. In addiction, reasonable periodic boundary conditions are successfully constructed, too. The presented RVE boundary conditions satisfy the Hill-Mandel condition and basic assumptions of the average-field theory and thus can be applied in the homogenization methods for heterogeneous Cosserat continuum
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Received: 23 April 2012
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2013, Vol. 34 
